reorienting mhd colliding flows: a shock physics mechanism ... · face, following haig et al....

Mon. Not. R. Astron. Soc. 000, 000–000 (0000) Printed 18 December 2019 (MN LATEX style file v2.2)

Reorienting MHD Colliding Flows:A Shock Physics Mechanism for Generating FilamentsNormal to Magnetic Fields

Erica L. Fogerty1?, Jonathan Carroll-Nellenback1, Adam Frank1, Fabian Heitsch2,Andy Pon3

1 206 Bausch & Lomb Hall, Department of Physics & Astronomy, University of Rochester, Rochester, New York, 14627, USA2 3255 Phillips Hall, Department of Physics & Astronomy, University of North Carolina, Chapel Hill, North Carolina, 27599, USA3 Department of Physics & Astronomy, University of Western Ontario, London, Ontario, N6A 3K7, Canada

Submitted 2016 September

ABSTRACT

We present numerical simulations of reorienting oblique shocks that form in thecollision layer between magnetized colliding flows. Reorientation aligns parsec-scalepost-shock filaments normal to the background magnetic field. We find that reori-entation begins with pressure gradients between the collision region and the ambientmedium. This drives a lateral expansion of post-shock gas, which reorients the growingfilament from the outside-in (i.e. from the flow-ambient boundary, toward the collidingflows axis). The final structures of our simulations resemble polarization observationsof filaments in Taurus and Serpens South, as well as the integral-shaped filamentin Orion A. Given the ubiquity of colliding flows in the interstellar medium, shockreorientation may be relevant to the formation of filaments normal to magnetic fields.

Key words: magnetohydrodynamics(MHD) – ISM: kinematics and dynamics – ISM:structure – ISM: clouds – stars: formation

1 INTRODUCTION

Colliding gas flows and filaments are commonly found instar forming regions. Converging flows have been detectedsurrounding molecular gas in Taurus (Ballesteros-Paredes,Hartmann & Vazquez-Semadeni 1999), the Sh 156 and NGC7538 molecular clouds (Brunt 2003), and star forming fila-ments in Serpens South (Kirk et al. 2013; Fernandez-Lopezet al. 2014). On the largest scales, they can arise from su-pernovae, energetic winds surrounding young stars and clus-ters, and the motion of galactic spiral arms through theintragalactic medium. On smaller scales, converging flowscan take the form of accretion flows. Similarly, filaments areubiquitous in star forming regions. Many have been found tocontain young protostellar cores (Andre et al. 2010; Arzou-manian et al. 2011; Polychroni 2012; Lee et al. 2014), andthus, are considered some of the earliest structures of starformation.

Observations of filaments indicate that they might betied to colliding flows. Measurements of velocity gradientsperpendicular to filaments (Kirk et al. 2013; Fernandez-

? E-mail:[email protected]

Lopez et al. 2014) have been interpreted as arising from in-fall onto the filaments (i.e. converging accretion flows). Dustpolarization maps show that the plane-of-sky component ofthe surrounding magnetic field also lies perpendicular to fil-aments (Goodman et al. 1992; Chapman et al. 2011; PlanckCollaboration et al. 2016). That both of these quantities alsoare aligned with low density ‘striations’ suggests that gas isconverging onto filaments, along magnetic fields (Palmeirimet al. 2013). Interestingly, fluid motions seem to change di-rection inside of filaments, so that the gas flows along fila-ments, internally (Kirk et al. 2013; Fernandez-Lopez et al.2014). Given that the uncertainty of dust polarization mea-surements increases with density (Goodman et al. 1992), thefield might actually change direction to become parallel in-side of filaments as well. Indeed, if the internal field did notbecome more or less parallel to the filament, external fieldlines would be bent away from normal due to drag betweeninternal fluid motions and the field (as shown in panel 4A,Fig. 1).

The gas motions and accompanying magnetic field ge-ometry associated with filaments have primarily been at-tributed to magneto-gravitational instability. In this concep-tualization, an over-dense region within a molecular cloud

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first becomes Jeans unstable (panel 1A, Fig. 1). Collapseis triggered and proceeds along magnetic field lines, as thegas is not yet magnetically supercritical (panel 2A). Onceenough mass accumulates for the region to become mag-netically supercritical, gas can begin to fall in perpendicu-lar to the field, as well. For magnetically supercritical fil-aments, this means collapse would then proceed along thefilament (panel 3A; Pon, Johnstone & Heitsch (2011); Ponet al. (2012); Toala, Vazquez-Semadeni & Gomez (2012)). Atthis point, the field would become distorted as it is draggeddown into the collapsing gas (panel 4A). That the magneticfield strength increases with density in collapsed gas (i.e.B ∝ n, n > 1000 cm−3; Troland & Heiles (1986); Crutcher(1999); Crutcher et al. (2010); Tritsis et al. (2015)) has com-monly been cited as evidence for this scenario.

An alternative explanation that does not require be-ginning with a Jeans unstable mass is the reorientation ofoblique magnetized shocks, which is the focus of the presentpaper. This model begins with the collision of marginallysupersonic gas along magnetic field lines (i.e. the path ofleast resistance). In the most general case, where the flowsmeet at a non-normal interface, it has recently been foundthat the central shock layer readjusts so that it becomes nor-mal to the upstream field (and oncoming flows). This effect,which has been reported by Kortgen & Banerjee (2015) andFogerty et al. (2016), is also consistent with observed fila-ment gas motions and field morphology (i.e. perpendicularexternal fluid motions and field lines, as well as parallel in-ternal fluid motions). Moreover, distortion of field lines bypassage through colliding flows shocks (cf. Chen & Ostriker(2014)) also produces a power law relationship of the mag-netic field strength with density (Heitsch et al. 2007; Hen-nebelle et al. 2008; Banerjee et al. 2009), consistent with theobservations described above.

To orient the reader, a schematic of the reorientationprocess is illustrated in the bottom panel of Figure 1. Forthe moderately magnetized cases of this paper (those runsthat have a β = 1, where β is the ratio of the thermal to mag-netic pressure), supersonic inflows that meet at an obliqueangle (θ) generate both an MHD fast shock (FS) and slowshock (SS) on either side of a contact discontinuity (CD;Fig. 1B, top/left). Between the FS and SS (region f − s),gas that moves parallel to the shock front (note the flowdirection is given by the black arrows) drags magnetic fieldlines away from the shock normal, whereas in region s − s,field lines bend toward the normal as they connect across theCD. Over time, the entire post-shock region reorients (rightpanel), where the grey-shaded region represents the growingfilament. As we will show, this process depends heavily onthe lateral ejection of material away from the growing fila-ment into the ambient medium (represented by the outwarddirected arrows, right hand column), which occurs due topressure gradients between the post-shock gas and the am-bient medium. The result is similar when the magnetic fieldis weakened (β = 10, Fig. 1B, bottom), notwithstanding theslight changes to the shock structure. That is, reorientationproduces a post-shock flow and field that has parallel com-ponents to the filament, internally (in regions f−s and f−c,in the β = 1 and β = 10 cases, respectively), and perpen-dicular components, externally. This MHD shock process isthe topic of the present paper.

We present a suite of 2D magnetized, colliding flows

1. 2.

3. 4.

FS SS CD

f-s s-c

FS SS/CD

α

α

γ

γ

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A.

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Before Reorientation After

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Figure 1. Mechanisms for generating filaments normal to mag-netic field lines. Top Panel. Magneto-gravitational collapse. Jeans

unstable gas will initially collapse along field lines (1-2). Once

enough mass accumulates in the resultant filament, mass can flowalong the filament and drag magnetic field lines inward (3-4). Bot-

tom Panel. Reorientation of magnetized oblique shocks. Upper-

case letters denote wave modes, and lowercase letters give regions(see text). Flow direction is given by the black arrows, and a rep-

resentative magnetic field line is shown in red. The left and rightpanels give the initial and reoriented structures, respectively. The

top and bottom rows give the moderate (β = 1) and weak field

(β = 10) cases of this paper. The grey shaded region representsthe growing filament.

simulations that test the effects of varying the magneticfield strength and the inclination angle of the collision in-terface on reorientation. We find that reorientation is pos-sible in all but the strongest magnetic field cases, resultingin post-shock filaments1 that approach a normal orienta-

1 In 2D, the result is actually the generation of perpendicular

sheets. Only in 3D could true filaments form. The basic MHDshock physics described here in 2D, however, can be extrapolated

to 3D. Fogerty et al. (2016) showed that fully 3D simulations also

exhibited reorientation.

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MHD Shock Reorientation 3

tion with respect to the upstream velocity and magneticfield. In addition, we show that fluid motions are highlyparallel to the filament within the shock bounded gas, andthat oblique, magnetized colliding flows naturally assume ans-shaped structure, reminiscent of the integral-shaped fila-ment (Bally et al. 1987; Johnstone & Bally 1999). Our paperis organized as follows. We begin with a description of ournumerical methods and model (Section 2). We then discuss1D shock solutions relevant to our work (Section 3) and ourkey results (Section 4). We finish with a discussion of ourfindings in Section 5.

2 METHODS

Our simulations were performed using AstroBEAR2 (Cun-ningham et al. 2009; Carroll-Nellenback et al. 2013). As-troBEAR is a massively parallelized, adaptive mesh refine-ment code designed for astrophysical contexts. The numeri-cal code solves the conservative equations of hydrodynamicsand magnetohydrodynamics, and includes a wide-range ofmultiphysics solvers. A sampling of these solvers include self-gravity, sink particles, various heating and cooling processes,magnetic resistivity, and radiative transfer. The AstroBEARcode is well tested (see, for example, Poludnenko, Frank &Blackman (2002); Cunningham et al. (2009); Kaminski et al.(2014)), under active development, and fully documentedby the University of Rochester’s computational astrophysicsgroup.

The present suite of simulations consists of two sets ofruns. The first was a pair of shock models that reviewedthe wave solutions across infinite hydrodynamic (hydro) andmagnetohydrodynamic oblique shocks, using an exact Rie-mann solver and HLLD solver, respectively. The shocks weregenerated by marginally supersonic flows (M = 1.5, whereM is the mach number) that collided at an oblique inter-face, following Haig et al. (2012) and Fogerty et al. (2016).These flows were injected along the x boundaries of a 2Dgrid so that they completely filled the domain (Fig. 2, toppanel). Boundary conditions in y were set to periodic. Theobliquity of the collision interface was given by the inclina-tion angle, θ, and was fixed at θ = 30◦. While these runswere performed on a 2D mesh, the fluid variables variedonly along the x−dimension. Thus, these runs provide thewave solutions across 1D oblique shocks. The second set ofruns was a parameter study of 2D finite magnetized collidingflows. In these runs, the flows were embedded in a stationaryambient medium of the same density and pressure (Fig. 2,bottom panel). The flows were again marginally supersonic(M = 1.5), and collided at an oblique interface, given bythe inclination angle θ. The inclination angle of the finiteruns varied between θ = 30◦ and 60◦. The complete suite ofsimulations is given in Table 1.

Self-gravity was not included in the present suite ofsimulations. Consequently, the simulations neglected gravi-tational collapse along filaments. The runs instead trackedthe formation and early evolution of filaments, while illus-trating the basic mechanism of reorientation. Cooling wasincluded in all of the finite colliding flows runs, following a

2 https://astrobear.pas.rochester.edu

θ20pc

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x

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Figure 2. Model diagrams. Top panel. Setup for the infinitecases. Incoming flows meet at an effectively infinite oblique shock,defined by the angle θ. Boundary conditions of the different box

sides are labeled. Magnetic field lines are represented by the redlines, and the flow is uniform everywhere along the collision in-

terface, in the direction given by the thick black arrows. Bottompanel. Setup for the finite cases. The colliding flows are now em-

bedded in a stationary ambient medium of the same density andpressure. The flows are 20 pc in diameter and collide at an obliquecollision interface, given by θ. The uniform magnetic field is againgiven by the red lines, and runs everywhere parallel to the flows.

modified Inoue & Inutsuka (2008) cooling curve. The mod-ification allowed the gas to cool to T = 10 K, appropriatefor ISM conditions (Ryan & Heitsch, in prep). The infinitecases did not include cooling, but instead used an adiabaticequation of state with γ = 5/3.

The parameters of each of the runs were chosen tomatch ideal ISM conditions (as discussed in Fogerty et al.(2016)). Thus, the runs were initialized at a uniform num-ber density of n = 1 cm−3 and temperature of T = 4931 K.At these densities and temperatures, the gas was initially inthermal equilibrium (for those runs that included cooling).

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Table 1. Suite of simulations.

Infinite/Finite Hydro/MHD β θ (◦) Domain Length (pc) Resolution AMR levels

Infinite† Hydro ... 30 1 2562 0Infinite† MHD 1 30 1 2562 0

Finite MHD .1 30 160 2562 2

Finite MHD 1 30 160 2562 2Finite MHD 10 30 160 2562 2

Finite MHD .1 60 160 2562 2

Finite MHD 1 60 320 5122 2Finite MHD 10 60 320 5122 2

†Did not include cooling

The speed of each inflow was v = 11 km s−1. For those runsthat included a magnetic field (cf. Table 1), the field wasuniform throughout the simulation domain and ran parallelto the flows. The strength of the field was set by β. In the1D MHD case, β = 1. For the finite colliding flows runs, βranged between β = 10 − .1. This is equivalent to a fieldstrength of B = 1.6− 16 µG, in line with current measure-ments of the global mean field of the ISM (B ≈ 1− 10 µG,Beck (2001); Heiles & Troland (2005)).

The infinite colliding flows runs had periodic boundaryconditions in y and inflow boundary conditions in x. Thelength of the square 2D domain was 1 pc on a side. Themesh was a fixed-grid at a resolution of 2562 and had acell size of 4x = .0039 pc. For the finite colliding flowsruns, the size of the square domain was chosen to be largeenough so that no gas or magnetic field lines left the boxover the course of the simulation (cf. Table 1). However,the effective resolution was held constant at a finest cellsize of 4xmin = .15625 pc. Boundary conditions were setto inflow where the flows were injected, and extrapolatingeverywhere else. The radius of the finite colliding flows wasr = 10 pc. The final simulation time for the finite runs wastsim = 12 Myr, with the exception of the β = 10, θ = 60◦

case, which was extended out until tsim = 16 Myr. Theinfinite cases were shorter at tsim = 1 Myr, the time it tookfor the shocks to reach the edge of the simulation domain.

3 INFINITE ADIABATIC OBLIQUE SHOCKS

Before we present the simulations of reorienting MHD col-liding flows, we briefly discuss the hydro and MHD shocksthat are generated by infinite, adiabatic colliding flows. Theresults of this section provide a framework for evaluatingthe shocks that are formed between finite, cooling collidingflows. Given this section is just a review of 1D oblique shocksolutions, the reader can feel free to jump ahead to our mainresults in Section 4.

3.1 Hydro Case

The hydro Riemann problem relevant to the present paperconsists of a constant density and pressure fluid that is sepa-rated by a discontinuous jump in velocity. In particular, thevelocity field converges on the central Riemann interface atan oblique incidence. Note, the inclination angle of the in-terface for both the infinite hydro and MHD run (discussed

below) was chosen to be θ = 30◦, to match the finite θ = 30◦

runs of Section 4.

As can be seen in Figure 3, this Riemann problem gen-erates two oblique shocks that are separated by a contactdiscontinuity. In addition to the characteristic density in-crease across each shock front, the top panel of Figure 3shows that velocity vectors bend away from the shock nor-mal across each shock. This occurs because only perpendic-ular components of upstream velocity vectors (v⊥) changeacross shocks. This leads to v⊥ → 0 in the downstreamgas. Note, if v⊥ 6= 0 in the post-shock gas, additional waveswould be generated behind the shocks, which would violatethe three-wave solution family of hydrodynamic Riemannproblems. Thus, post-shock gas flows exactly parallel to eachshock front. In other words, oblique shocks generate shear.The various fluid variables across the wave modes are givenin the bottom panel of Figure 3.

3.2 MHD Case

The addition of a uniform magnetic field that is parallel tothe flows modifies the shock structure just described. Forthis case, two oblique shocks are generated on either sideof the contact discontinuity (Fig. 4). Given Alfven modescannot be generated in 1D, the forward-most shock can beidentified with the MHD fast shock (FS), which is trailedby the slow shock (SS). As before, incoming velocity vectorsare deflected away from the shock normal across the outer,FS (Fig. 4). However, now these redirected velocity vectorsencounter the magnetic field. The collision between the flowand the field causes the field to also bend away from theshock normal across the FS, as the field and fluid are per-fectly coupled in ideal MHD. The result is an amplificationof the field across the FS, visible by both the color of thefield lines, which increase in strength from white to red (Fig.4, top panel), as well as the amplification of the parallel fieldcomponent (B//) across the FS (bottom panel). Given thefield is tied across the contact discontinuity (CD), it even-tually must turn back toward the shock normal. This givesrise to the inner, SS, where the field again switches direc-tion. However, in contrast to the FS, gas that passes the SSis stagnated. This is visible by zero velocity gas motions inthe region s−s (defined in Fig. 1, bottom panel). Lastly, wenote that reorientation fundamentally cannot occur in 1D,given the symmetry in the initial conditions.

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//

n

nn

Figure 3. Numerical solution of the infinite hydrodynamic Rie-

mann problem. Top panel shows number density (n(cm−3)) withoverlaid velocity vectors that are scaled by magnitude. Bottompanel gives the various fluid variables across the waves. Perpen-

dicular and parallel components of velocity (v⊥ and v//, respec-tively) are in units of km s−1, number density in cm−3, and

pressure (P ) in K cm−3. Note, pressure has been scaled to fit on

the y−axis, where P = (P − 4931) × 10−3.

4 FINITE OBLIQUE SHOCKS, WITHCOOLING

We now turn to our finite magnetized colliding flows runsto address the issue of reorientation of oblique shocks. Note,this section differs from the last in that now the flows areembedded in a stationary ambient medium. We begin bydiscussing the effects of varying β and θ on the morphol-ogy of reoriented flows. We then move on to discussing thetemporal evolution of each of the cases, again focusing onmorphological changes over the course of the simulations.

n

nn

Figure 4. Numerical solution of the infinite MHD Riemann prob-lem. Top panel is a plot of number density (n(cm−3)) with over-

laid magnetic field lines and velocity vectors. Field lines increasein strength from white to red and velocity vectors are again scaledby magnitude. Bottom panel gives the fluid variables across thewaves. Units are the same as in Figure 3, with the addition of the

perpendicular and parallel magnetic field components (B⊥ andB//, respectively), given in µG.

4.1 The Effects of Varying β and θ onReorientation

In the finite colliding flows scenario, post-shock motionsno longer strictly adhere to the shear flow predicted bythe infinite shock solutions of Section 3. Pressure gradientsnow exist between post-shock gas and the external ambi-ent medium, which forces material laterally outwards, awayfrom the collision region. Given reorientation does not occurin the infinite case, this lateral motion is a key component ofreorientation. This is illustrated by the fact that reorienta-tion does not occur when material is prevented from leavingthe collision region, as in the strong field (β = .1) cases.

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Plots of number density show that when β = .1, for inclina-tion angles of either θ = 30◦ or 60◦, magnetic field lines arestrong enough to resist ejection of material from the collisionregion (Fig. 5, top panel). Any material that does manageto escape the collision region travels parallel to the collidingflows, along the field lines, and is deposited in what we callthe ‘trailing arms’ of the filament – a prominent feature offinite, oblique, magnetized colliding flows (see red circles inFig. 5, top-left panel). Indeed, the field is so strong in thesecases that a post-shock shear flow is also inhibited, as thefield effectively resists motion perpendicular to it. Instead,post-shock material is delivered directly onto the growingfilament, where it continues to collect, cool, and compressover the course of the simulation. This results in a smoothand flat filament, as turbulent sub-structure (induced fromthe thermal instability, e.g.) is also effectively inhibited.

The behavior begins to change as the magnetic field isweakened. When β is increased to 1, the θ = 30◦ case ex-hibits a large-scale reorientation. This is illustrated in Figure5 (middle row, left panel), where we see an initially inclinedfilament has reoriented to become more or less normal tothe oncoming flows by t = 6.6 Myr (note the black ref-erence line in the figure, which shows the initial filamentorientation). As in the infinite version of this case, an outershock layer forms that diverts incoming flows either diago-nally ‘up’ or ‘down’, depending on the upstream interfaceorientation (cf. Section 3.2). However, across the second, in-ner shock (region s− s), gas is falling onto the long axis ofthe filament, along magnetic field lines. This is in contrastto the infinite case, where fluid motions were absent in thisregion, and thus, these motions are arising from cooling. Theresult is the formation of a post-shock flow that has paral-lel components to the filament in both the f − s and s − cregions.

Near the top and bottom of the filament (i.e. near theflow-ambient boundary), and across the CD, the velocityvectors become aligned so that they are pointing along y, outinto the ambient medium. That is, the flow switches frombeing a shear flow across the FS, to being directed outwardsinto the ambient medium in the entire f − f region (nearthe flow-ambient boundary). This is due to pressure gradi-ents between the collision region and the ambient medium.The ejection of material from the over-pressurized collisionregion into the ambient medium drives arcs in the magneticfield, whose tension impedes further lateral flow and trapsthe ejected gas (see Fogerty et al. (2016) for an analyticaldescription of this process). This trapped gas travels alongthe magnetic field line arcs, as shown by the correspondingvelocity vectors in Figure 5, where it collects in the trailingarms. This three-step process, namely, 1) post-shock ejec-tion from the collision region into the ambient medium, 2)the bending of the magnetic field lines into arcs, and 3)the redirection of incoming flows along the arcs to collectin the trailing arms of the filament, produces an ‘s-shaped’filamentary structure.

As the inclination angle is steepened to 60◦ for the β = 1case, the same trends develop. Namely, material is deflectedaway from the shock normal across the FS, ejected from thecollision region into the ambient medium, and an s-shapedfilament forms with a similar degree of reorientation by t =5Myr. While the higher obliquity shocks of this run produceweaker post-shock compression and thus a wider f−s region,

changing the inclination angle does not appear to drasticallyalter the degree of reorientation for the moderate field, β = 1cases.

As the field is weakened further in the β = 10 runs,the 30◦ case reorients to a similar degree, but reorienta-tion is enhanced in the 60◦ case (Fig. 5, bottom row). Wealso see that slightly different filamentary structures form,as there are no longer slow shocks present in the filaments.This means that by β = 10, the shock solutions have effec-tively approached the 1D hydro solutions (away from theflow-ambient boundary), as they must, in the limit of weakmagnetic field. Furthermore, there are no longer s − s re-gions (marked by a stagnate velocity field), where materialcan expand away from the collision region due to pressuregradients alone. Instead, incoming gas is quickly shuntedaway from the collision region as it passes through the sin-gle oblique shock on either side of the CD. As this materialleaves the collision region, it drags magnetic field lines awaywith it. As the plots show, the weaker field is dragged tofurther distances, and thus the trailing arms extend fartheraway into the ambient medium from the main filament body(beyond the plot boundaries).

4.2 Temporal Evolution of the Flows

We now turn to the temporal evolution of the flows. We willagain be focusing on density plots with overlaid velocity vec-tors and magnetic field lines, beginning with the strongerfield (β = 1) cases. Figure 6 shows the evolution of theβ = 1, θ = 30◦ case. As can be seen in the t = .49 Myrpanel, the bulk properties of the flow are similar to the infi-nite MHD case (Section 3.2), at early times. That is, a shearflow is established across the outer, FS, and negligible fluidmotions occur inside of region s− s. Over time, post-shockcooling triggers inflow along the field lines onto the CD ofthe forming filament (t = 2.1 Myr). Additionally, this timepanel shows that the fast shocks stall (near the top flow-ambient boundary for the right FS, and near the bottomfor the left FS). This is due to a decrease in thermal pres-sure support behind the shocks as material escapes into thelower pressure ambient medium. The result of these stalledshock fronts is the reorientation of the outer shock layers,as those regions that are not stalled continue to propagateaway from the collision region. This leads to the outer shocklayers becoming normal to the oncoming flows.

As can be seen in the figure (and even better in theanimations online3), reorientation of the inner shock layer(i.e. region s − s) also begins with the lateral ejection ofmaterial from the collision region. That is, reorientation oc-curs from the outside-in – beginning near the flow-ambientboundary and moving toward the colliding flows axis byt = 12 Myr. This occurs as material is delivered along the‘z-shaped’ magnetic field lines near the colliding-flows axisnearly vertically onto the long axis of the filament. Whenthe inclination angle is steepened to θ = 60◦ for the samevalue of β = 1, the evolution is qualitatively similar (Fig.7).

3 See the online supplementary material, as well as the follow-

ing youtube channel: https://www.youtube.com/channel/UCE

mUg0BdCyPC3QnKdNDJq1w

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β=1

θ=30° θ=60°

β=.1

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Figure 5. Density plots with overlaid velocity vectors and magnetic field lines. The legend gives number density in units of cm−3.

Velocity vectors are scaled by magnitude, and field lines increase in strength from white to black. On left are the 30◦ runs, which increase

in β from top to bottom. On right are the 60◦ runs, which also increase in β from top to bottom. The black reference line traces theinitial collision interface of the given run. The trailing arms of the filament (discussed in text) are present in each of the panels, but are

illustrated for clarity by the red circles in the upper-left panel only.

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n n n

Figure 6. Evolution of the β = 1, θ = 30◦ case. All units are the same as in Figure 5.

nn n n

Figure 7. Evolution of the β = 1, θ = 60◦ case. All units are the same as in Figure 5. A black reference line has been added that tracesthe initial collision interface.

As the field is weakened to β = 10, the largest dif-ference that occurs in the evolution is the appearance of avacated inner region along the filament’s long axis (FLA)as material preferentially collects around the top and bot-tom of the filament (i.e. near the flow-ambient boundary),as well as just exterior to the FLA (see Figures 8 and 9,middle panels). This arises from the extreme amplificationof the field along the CD as field lines are stretched by theshear flow (recall, the color of the field lines increases fromwhite to black with increasing field strength). By the lasttime panel, in both the θ = 30◦ and 60◦ cases, gas hassuccessfully collapsed onto the FLA, and the internal highdensity regions of the filament have begun to reorient, againfrom the outside-in. Within the region f − f , the flow andthe field are highly parallel to the filament, and the entirestructure (filament+trailing arms) has assumed an s-shapedgeometry.

While this overall evolution is the same between thetwo β = 10 cases, the external flow field in the θ = 60◦ caseat t = 15.8 Myr is unlike any of the other runs. Velocityvectors show that material entering from the left is directeddownwards as it approaches the filament, and that materialentering from the right is directed upwards. Note, this is theopposite flow pattern that the oblique shocks establish alone

(see earlier time panels), indicating that the flow is travelingalong bowed magnetic field lines. Such an asymmetric flowis necessary to generate a torque on the filament. This couldexplain why the β = 10, θ = 60◦ case reorients more thanthe β = 1, θ = 60◦ case.

5 DISCUSSION

We have presented an MHD shock mechanism capable of re-orienting filaments formed via colliding flows. This processwas identified previously in fully 3D simulations of magne-tized colliding flows that included turbulence, self-gravity,cooling, and oblique shocks at the collision interface (Fogertyet al. 2016). In that work, large-scale reorientation of molec-ular gas had occurred for a highly oblique run (Fig. 10).Reorientation of the collision interface of 3D, magnetized,oblique colliding flows was also recently reported by Kortgen& Banerjee (2015). By running the simulations in 2D, with-out gravity, we have shown that the mechanism of reorienta-tion is robust. Moreover, that hydro simulations of obliquecolliding flows do not exhibit reorientation (both in 2D, aswell as 3D, Haig et al. (2012), Haig & Heitsch, in prep), indi-cates that magnetic fields play a crucial role in the process.

As we have shown, reorientation begins with the lateral

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n n n


n n n


ejection of material away from the post-shock collision re-gion between colliding flows. Without magnetic fields, ejectawould continue to push out into the ambient medium untilits ram pressure came into balance with the thermal pres-sure of the environment. With magnetic fields, this mate-rial is funneled back down along bowed magnetic field lines,toward the colliding flows surface. This produces what wehave called, ‘trailing arms’ of the filament. Additionally, es-caped gas from the collision region into the ambient mediumtranslates into a loss of post-shock pressure support, result-ing in stalled outer shocks. This led to the reorientation ofthe outer shocks, which is also seen in hydro. The differencelies in the reorientation of the densest regions of the filament(i.e. along the CD of the collision region), which does not oc-cur without the magnetic field. Instead, the shear flow setupacross hydro oblique shocks generates instabilities (i.e. KHmodes) along the interface. These instabilities in turn pro-duce a ‘stair-casing’ structure, but not a coherent filamentthat reorients (Haig et al. 2012). Hennebelle (2013) showedthat in order to build a coherent filament in a shear flow, amagnetic field must be present.

The role of the magnetic field in reorienting the internallayers of the filament is the delivery of material along ‘z-shaped’ magnetic field lines within the collision zone, nearthe colliding flows axis (red box, Fig. 11, left panel). Note,

these field lines have not been ‘blown-out’ into arcs from thelateral post-shock ejection (as seen in the yellow box of Fig.11, left panel), and thus deliver material nearly verticallyonto the growing filament. Thus, reorientation begins withthe lateral escape of gas from the collision region, and movestoward the center of the collision region over time. As themagnetic field is weakened, torque on the collision regionmay play an additional role in the reorientation process. Aswe have seen, the β = 10, θ = 60◦ case reoriented to agreater extent than the stronger field β = 1, θ = 60◦ case,and this coincided with a large-scale asymmetric flow ontothe filament. The mismatch in incoming x-momenta ontothe filament can be seen in the right-hand panel of Figure11, which illustrates the effect for the smaller inclinationangle case, β = 10, θ = 30◦. As the figure shows, there is anasymmetric loss of material from the collision region acrossthe CD in the weak field cases (yellow circles), which couldlead to a net torque being generated by the bounded flowthat remains (red arrows).

Lastly, we have demonstrated that reorientation pro-duces structures that are physically relevant for star-formingregions. In particular, we have shown that under realisticISM magnetic field strengths, reorientation generates fila-ments perpendicular to their background magnetic fields, aswell as exhibit velocity motions that switch from being per-

c© 0000 RAS, MNRAS 000, 000–000


Figure 10. Evolution of the 3D β = 10, θ = 60◦ case, with self-gravity. Image taken from Fogerty et al. (2016). The colors representcolumn density, and increase from blue to red. See Fogerty et al. (2016) for details.

Figure 11. Left panel shows the dominant mechanism of reorientation for the β = 10 cases. Namely, field lines that assume a bowed

structure near the flow-ambient boundaries (yellow box) deliver material away from the collision region onto the trailing arms, whereas‘z-shaped’ field lines that reside closer-in to the colliding flows axis (red box) deliver material directly onto the filament. This differentialdelivery results in an outside-in reorientation of the filament. Note, the legend gives number density in units of cm−3, here called ‘rho’.

Right panel shows that in the weaker field cases, material escapes from the collision region asymmetrically across the CD (yellow circles),due to the shear flow. The barred red arrows delineate the subset of oncoming material that makes it into the collision region. This leads

to a mismatch in the x−momenta being delivered onto the filament, and thus, a torque in the direction of reorientation.

pendicular externally to parallel internally. These featuresare consistent with observations of star-forming filaments(Kirk et al. 2013; Palmeirim et al. 2013; Fernandez-Lopezet al. 2014; Planck Collaboration et al. 2016). Additionally,we have shown that filaments formed via finite, magnetizedoblique shocks naturally assume an s-shaped geometry.

ACKNOWLEDGMENTS

This research was supported in part by the US Departmentof Energy through grant GR523126, the National ScienceFoundation through grant GR506177, and the Space Tele-scope Science Institute through grant GR528562. A.P. wouldalso like to acknowledge that partial salary support wasprovided by the Canadian Institute for Theoretical Astro-physics (CITA) National Fellowship.

REFERENCES

Andre P. et al., 2010, A&A, 518, L102Arzoumanian D. et al., 2011, A&A, 529, L6Ballesteros-Paredes J., Hartmann L., Vazquez-SemadeniE., 1999, ApJ, 527, 285

Bally J., Langer W. D., Stark A. A., Wilson R. W., 1987,ApJl, 312, L45

Banerjee R., Vazquez-Semadeni E., Hennebelle P., KlessenR. S., 2009, MNRAS, 398, 1082

Beck R., 2001, SSRv, 99, 243Brunt C. M., 2003, ApJ, 583, 280Carroll-Nellenback J. J., Shroyer B., Frank A., Ding C.,2013, Journal of Computational Physics, 236, 461

Chapman N. L., Goldsmith P. F., Pineda J. L., ClemensD. P., Li D., Krco M., 2011, ApJ, 741, 21

Chen C.-Y., Ostriker E. C., 2014, ApJ, 785, 69

c© 0000 RAS, MNRAS 000, 000–000


Crutcher R. M., 1999, ApJ, 520, 706Crutcher R. M., Wandelt B., Heiles C., Falgarone E.,Troland T. H., 2010, ApJ, 725, 466

Cunningham A., Frank A., Varnire, P. M. S., Jones T.,2009, ApJS, 182, 519

Fernandez-Lopez M. et al., 2014, ApJL, 790, L19Fogerty E., Frank A., Heitsch F., Carroll-Nellenback J.,Haig C., Adams M., 2016, MNRAS, 460, 2110

Goodman A. A., Jones T. J., Lada E. A., Myers P. C.,1992, ApJ, 399, 108

Haig C. M., Heitsch F., Carroll J., Frank A., 2012, in Amer-ican Astronomical Society Meeting Abstracts, Vol. 219,American Astronomical Society Meeting Abstracts #219,p. 349.02

Heiles C., Troland T. H., 2005, ApJ, 624, 773Heitsch F., Slyz A. D., Devriendt J. E. G., Hartmann L. W.,Burkert A., 2007, ApJ, 665, 445

Hennebelle P., 2013, A&A, 556, A153Hennebelle P., Banerjee R., Vazquez-Semadeni E., KlessenR. S., Audit E., 2008, A&A, 486, L43

Inoue T., Inutsuka S.-i., 2008, ApJ, 687, 303Johnstone D., Bally J., 1999, ApJl, 510, L49Kaminski E., Frank A., Carroll J., Myers P., 2014, ApJ,790, 70

Kirk H., Myers P. C., Bourke T. L., Gutermuth R. A.,Hedden A., Wilson G. W., 2013, ApJ, 766, 115

Kortgen B., Banerjee R., 2015, MNRAS, 451, 3340Lee K. I. et al., 2014, ApJ, 797, 76Palmeirim P. et al., 2013, A&A, 550, A38Planck Collaboration et al., 2016, A&A, 586, A136Poludnenko A. Y., Frank A., Blackman E. G., 2002, ApJ,576, 832

Polychroni D., 2012, in 10th Hellenic Astronomical Confer-ence, Papadakis I., Anastasiadis A., eds., pp. 24–24

Pon A., Johnstone D., Heitsch F., 2011, ApJ, 740, 88Pon A., Toala J. A., Johnstone D., Vazquez-Semadeni E.,Heitsch F., Gomez G. C., 2012, ApJ, 756, 145

Toala J. A., Vazquez-Semadeni E., Gomez G. C., 2012,ApJ, 744, 190

Tritsis A., Panopoulou G. V., Mouschovias T. C., TassisK., Pavlidou V., 2015, MNRAS, 451, 4384

Troland T. H., Heiles C., 1986, ApJ, 301, 339

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